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Simplifying 64x6 = 27 + -11x3 + 1 Reorder the terms: 64x6 = 27 + 1 + -11x3 Combine like terms: 27 + 1 = 28 64x6 = 28 + -11x3 Solving 64x6 = 28 + -11x3 Solving for variable 'x'. Reorder the terms: -28 + 11x3 + 64x6 = 28 + -11x3 + -28 + 11x3 Reorder the terms: -28 + 11x3 + 64x6 = 28 + -28 + -11x3 + 11x3 Combine like terms: 28 + -28 = 0 -28 + 11x3 + 64x6 = 0 + -11x3 + 11x3 -28 + 11x3 + 64x6 = -11x3 + 11x3 Combine like terms: -11x3 + 11x3 = 0 -28 + 11x3 + 64x6 = 0 Begin completing the square. Divide all terms by 64 the coefficient of the squared term: Divide each side by '64'. -0.4375 + 0.171875x3 + x6 = 0 Move the constant term to the right: Add '0.4375' to each side of the equation. -0.4375 + 0.171875x3 + 0.4375 + x6 = 0 + 0.4375 Reorder the terms: -0.4375 + 0.4375 + 0.171875x3 + x6 = 0 + 0.4375 Combine like terms: -0.4375 + 0.4375 = 0.0000 0.0000 + 0.171875x3 + x6 = 0 + 0.4375 0.171875x3 + x6 = 0 + 0.4375 Combine like terms: 0 + 0.4375 = 0.4375 0.171875x3 + x6 = 0.4375 The x term is 0.171875x3. Take half its coefficient (0.0859375). Square it (0.007385253906) and add it to both sides. Add '0.007385253906' to each side of the equation. 0.171875x3 + 0.007385253906 + x6 = 0.4375 + 0.007385253906 Reorder the terms: 0.007385253906 + 0.171875x3 + x6 = 0.4375 + 0.007385253906 Combine like terms: 0.4375 + 0.007385253906 = 0.444885253906 0.007385253906 + 0.171875x3 + x6 = 0.444885253906 Factor a perfect square on the left side: (x3 + 0.0859375)(x3 + 0.0859375) = 0.444885253906 Calculate the square root of the right side: 0.666997192 Break this problem into two subproblems by setting (x3 + 0.0859375) equal to 0.666997192 and -0.666997192.Subproblem 1
x3 + 0.0859375 = 0.666997192 Simplifying x3 + 0.0859375 = 0.666997192 Reorder the terms: 0.0859375 + x3 = 0.666997192 Solving 0.0859375 + x3 = 0.666997192 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0859375' to each side of the equation. 0.0859375 + -0.0859375 + x3 = 0.666997192 + -0.0859375 Combine like terms: 0.0859375 + -0.0859375 = 0.0000000 0.0000000 + x3 = 0.666997192 + -0.0859375 x3 = 0.666997192 + -0.0859375 Combine like terms: 0.666997192 + -0.0859375 = 0.581059692 x3 = 0.581059692 Simplifying x3 = 0.581059692 Reorder the terms: -0.581059692 + x3 = 0.581059692 + -0.581059692 Combine like terms: 0.581059692 + -0.581059692 = 0.000000000 -0.581059692 + x3 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.Subproblem 2
x3 + 0.0859375 = -0.666997192 Simplifying x3 + 0.0859375 = -0.666997192 Reorder the terms: 0.0859375 + x3 = -0.666997192 Solving 0.0859375 + x3 = -0.666997192 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0859375' to each side of the equation. 0.0859375 + -0.0859375 + x3 = -0.666997192 + -0.0859375 Combine like terms: 0.0859375 + -0.0859375 = 0.0000000 0.0000000 + x3 = -0.666997192 + -0.0859375 x3 = -0.666997192 + -0.0859375 Combine like terms: -0.666997192 + -0.0859375 = -0.752934692 x3 = -0.752934692 Simplifying x3 = -0.752934692 Reorder the terms: 0.752934692 + x3 = -0.752934692 + 0.752934692 Combine like terms: -0.752934692 + 0.752934692 = 0.000000000 0.752934692 + x3 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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